Schematic representation of the alternative model with activation of B cells by virus. The blue line denotes the change from the baseline model in Fig. 1.

Schematic representation of the influenza A virus infection model. A black arrow denotes either differentiation or activation. A dashed line between cells denotes cell-cell interactions.

Schematic representation of the alternative model with a separate population of licensed DC (D_L) added. The blue lines denote the changes from the baseline model in Fig. 1.

Drug responses. Viral kinetics with administration of a drug either limiting viral infection (amantadine), limiting viral production (neuraminidase inhibitor or RNA polymerase inhibitor), or both types of drugs. The timing of the administration of the drug since the infection is denoted by T_drug (dashed line). The efficacy of drug limiting viral infection is denoted as ɛ₁ and that of drug limiting viral production is denoted as ɛ₂. Containment of viral spread is slightly enhanced when the drug limiting viral production is used. No differences in viral kinetics were observed under either condition when drug was administered 3 or more days after viral inoculation. Combination of both types of drugs can enhance viral clearance when they are administrated within 2 days.

Immune memory response. (a) Kinetics of viral load in the secondary response with immune memory of antibody only (top left panel), CD8 T cells only (top right panel), and both antibody and CD8 T cells. The initial antibody titer is fixed as 10² and the initial effector CD8 T-cell level [T_E(0)] is changed from 0 to 10⁵ (bottom left panel). The initial antibody level is fixed as a 10³ titer and the initial level of CD8 T cells is changed from 0 to 10⁵ (bottom right panel). (b) Time to clear the virus (t_clear) as a function of initial antibody titer, A(0), initial level of effector CD8 T cells, T_E(0), initial level of airway/lung resident effector CD8 T cells, T_*E(0), and initial level of effector CD4 T cells, H_E(0). Time to clear the virus is defined as time for the viral load to reach 1 EID₅₀/ml since infection. The light blue horizontal line indicates one-half the time to clear virus in the absence of any memory responses.

Sensitivity analysis. Data show the time to clear virus with a 50% increase (dots) or 50% decrease (squares) of each parameter in comparison with the control set of parameters (solid line) for the control model (a) and for the alternative model with the assumption of activation of B cells by the virus (b). (a) Changes in death rates of uninfected and infected epithelial cells (δ_E, δ_E*), initial level of uninfected epithelial cells (E₀), infection rate of epithelial cells (β_E), CD8 T-cell migration factor (γ), CD8 T-cell migration delay (τ_T), viral production rate (π_v), rate of CD8 T-cell killing (k_E), death rate of uninfected DC (δ_D), and infection rate of DC (β_D) had minimal effects on time to viral clearance. An increase in the viral clearance rate (c_v), the rate of antibody neutralization (k_v), initial level of DC (D₀), or the antigen processing rate (k_D) significantly reduces the time to clear virus. Increase in the death rate of infected DC (δ_D*) or mature DC (δ_DM) or in the migration delay of virus-loaded DC (τ_D) significantly prolongs the infection (a). In the alternative model, each increase in the initial level of uninfected epithelial cells (E₀) and in the rate of viral production (π_v) results in the largest changes in the duration of infection.

Absence of each arm of the immune response. The kinetics of uninfected and infected epithelial cells are shown in the left panels (a, c, e, g, and i), viral load (EID₅₀/ml) is shown in the right panels (b, d, f, h, and j); data for short-lived and long-lived plasma cells (k) and antibody titers (l) are also shown. The absence of CD8 T-cell response in primary influenza virus infection results in slower clearance of infected epithelial cells (c, compare with panel a) and delay of the viral clearance (d), compared to control observations (red dots in panel b). In the absence of an IAV-specific antibody response in primary influenza virus infection, the kinetics of infected, uninfected, and infected epithelial cells are not changed (a and e). However, the absence of antibodies results in slower viral clearance (d) than control observations. The absence of both CD8 T-cell and B-cell responses results in infected epithelial cells persisting longer (g) due to the lack of cytotoxic CD8 T-cell response and sustained viral load (h). In the absence of CD4 T-cell help, viral kinetics results in a 2-day delay in viral clearance (j). Differentiation of long-lived plasma cells does not occur without CD4 T-cell help (k), which results in decay of the antibody level without CD4 T-cell help (l). Red dots with standard deviations in panel l denote serum influenza virus-specific IgG kinetics from five MHC class II-deficient mice (see reference 44).

Model solution. (A to J) Numerical solutions of the model were compared with our new experimental data (influenza virus-specific CD8 T cells in the lung compartment) and published experimental data (viral load, CD8 T cells in the lymphatic compartment [spleen and lymph node]) (62), and other published data (10, 44). Viral load and influenza virus-specific CD8 T-cell kinetics are from C57BL/6 mice intranasally infected with 10⁵ 50% EID₅₀ of influenza A/HKx31 as previously reported by our lab in reference 62. Viral titers in lungs were measured by hemagglutination assay, after expansion in embryonated eggs; the EID₅₀ was calculated using the Reed-Muench equation. Influenza virus-specific CD8 T cells were detected via flow cytometry in the spleen, mediastinal LN, and lung by PE-conjugated H-2D^b MHC class I/NP_366-374 tetramer staining (62). We used a scale factor of 10 to extrapolate total influenza virus-specific CD8⁺ T-cell counts from NP_366-374-specific CD8 T cells. G. T. Belz and W. R. Heath (Immunology Division, The Walter and Eliza Hall Institute of Medical Research, Melbourne, Victoria 3050, Australia) kindly provided us with raw data for the kinetics of virus-loaded DC in LN (see Fig. 1A in reference 10). Lymphatic compartment DC kinetics are from C57BL/6 mice intranasally infected with 10² PFU of HKx31 and determined in mediastinal LNs treated with collagenase/DNase to form single-cell suspensions which were then cultured with a lacZ-inducible hybridoma-specific for influenza virus NP and enumerated for β-galactosidase-producing cells (10). T. D. Randall (Trudeau Institute, Saranac Lake, NY) kindly provided raw data of the kinetics of serum antibody (see Fig. 5A in rerference 44). Serum antibody kinetics are from C57BL/6 mice intranasally infected with 100 egg infectious units of influenza A/PR8/34, and influenza virus-specific IgG titers were determined by enzyme-linked immunosorbent assay (44). (K) Viral kinetics were for different initial viral loads. As initial viral load increases, the peak viral load appears earlier. The initial slope of the ramp-up phase does not depend on the initial viral load. The analytical expression (see Materials and Methods) for the initial slope of the viral load increase (solid black line) was compared with the solutions. The model and a differential equation simulator (DEDiscover) is available for download at https://cbim.urmc.rochester.edu/software/dediscover/.